CN107102298B - Radar Covariance Matrix Reconstruction Beamforming Method Based on Iterative Mutual Coupling Correction - Google Patents

Abstract

The invention discloses a radar covariance matrix reconstruction beamforming method based on iterative mutual coupling correction. The idea is to determine a uniform circular array, which includes M array elements, and there are Q signal sources, Q signal sources transmit Q incident signals to the uniform circular array, and the Q incident signals include 1 desired signal and Q-1 interference signals; obtain the sampling covariance matrix R of the uniform circular array and perform characterization Decompose to obtain M eigenvalues; calculate the MUSIC spectrum of the signal with the incident direction (θ, φ), and then set the initial value of the mutual coupling matrix of the uniform circular array, and then obtain the initial values of Q azimuth angles of the Q incident signals, and The final mutual dual matrix of the uniform circular array is obtained respectively and the final azimuths of the Q incident signals Then calculate the interference-plus-noise covariance matrix of the reconstructed uniform circular array Then the weight vector of the adaptive beamformer of the uniform circular array is obtained, and the reconstruction of the interference-plus-noise covariance matrix of the uniform circular array based on iterative mutual coupling correction is completed.

Description

Radar Covariance Matrix Reconstruction Beamforming Method Based on Iterative Mutual Coupling Correction

technical field

The invention belongs to the technical field of conformal array antenna beamforming, and particularly relates to a radar covariance matrix reconstruction beamforming method based on iterative mutual coupling correction, which is suitable for solving the problem that the adaptive beamformer is robust due to the strong expected signal power in sampling samples The problem of performance degradation, and the performance degradation of the beamformer when considering the mutual coupling effect, and the robust performance of the beamformer is improved while considering the mutual coupling effect between array elements.

Background technique

Conformal arrays have been widely used due to their advantages of electromagnetic concealment, large scanning angle, small load weight, and no interference with the aerodynamic flow field of flying objects; however, conformal array beamforming technology is widely used in theoretical research and development applications face several difficulties. First of all, the traditional beamforming technology has the defect of insufficient robustness in the actual environment, which still exists when it is applied to the conformal array; in addition, when the signal received by the array antenna is transmitted inside the receiving unit, the mutual coupling effect between the array elements Can not be ignored. However, the complex element distribution of the conformal array increases the difficulty of accurate analysis and modeling of its electromagnetic characteristics, making the mutual coupling correction of the conformal array very difficult. Therefore, under the premise of giving full play to the advantages of conformal arrays, it is an urgent problem to design a robust beamforming algorithm and break through the limitations of mutual coupling factors on beamformers.

Theoretical research on adaptive beamforming technology began in the 1960s. In 1969, Capon proposed the Minimum Variance Distortionless Response (MVDR) criterion, which minimizes the output power of the array while ensuring the desired signal gain, and provides a theoretical basis for the beamformer to suppress interference. In the 1970s, researchers proposed the sampling matrix inversion (SMI) algorithm, which uses snapshots of array received signals to estimate the interference-plus-noise covariance matrix, which can adaptively suppress interference signals. In 1974, Brennan et al. derived the probability density function of the output signal-to-interference-noise ratio of the SMI beamforming algorithm, and gave the relationship between the performance of the adaptive algorithm and the number of training samples.

In many practical application fields, the performance of the adaptive beamformer will be affected by various error factors, such as signal observation error, receiving channel error, array element position error, etc. These errors will cause the steering vector mismatch of the array antenna receiving signal , leading to the degradation of the performance of the beamforming algorithm; and when the sample snapshot contains the desired signal, the mismatch of the steering vector has a particularly significant impact on the performance of the adaptive beamformer.

In 1991, Benjamin Friedlander and W Anthony J. Weiss proposed a DOA estimation method when there is mutual coupling between array elements, which can accurately estimate the DOA of the signal's direction of arrival and the mutual coupling between uniform circular arrays, but The DOA estimation method in the presence of mutual coupling between array elements has not been applied in the field of adaptive beamforming technology; in 2012, Gu proposed a beamforming method based on the reconstruction of the interference plus noise covariance matrix. The constructed covariance matrix replaces the expected polluted sampling covariance matrix to calculate the adaptive weight vector. Although it has better performance when the expected signal power is stronger, this method has the following two problems in practical applications: first , this method requires that the array configuration is known precisely, and the only allowable error is the observation angle error, and the performance is greatly degraded when considering the mutual coupling effect; second, the method is computationally complex when reconstructing the interference-plus-noise covariance matrix The degree is very large, which restricts the real-time performance of the algorithm.

Contents of the invention

In view of the deficiencies in the prior art above, the purpose of the present invention is to propose a radar covariance matrix reconstruction beamforming method based on iterative mutual coupling correction, which is based on the iterative mutual coupling correction radar covariance matrix reconstruction beamforming method The incident angle of the signal and the mutual coupling matrix of the uniform circular array are iteratively estimated, combined with the reconstruction method of the interference plus noise covariance matrix, the reconstruction of the interference plus noise covariance matrix and the correction of the desired steering vector are completed, and an array element A more robust beamformer in the presence of mutual coupling.

In order to achieve the above object, the present invention adopts the following technical solutions to achieve.

A radar covariance matrix reconstruction beamforming method based on iterative mutual coupling correction, comprising the following steps:

Step 1, determine the uniform circular array, the uniform circular array includes M array elements, there are Q signal sources within the set range of the uniform circular array, and the Q signal sources transmit Q incident signals to the uniform circular array, and the Q incident signals The signal contains 1 desired signal and Q-1 interference signals;

Obtain the sampling covariance matrix R of the uniform circular array, and perform eigendecomposition on the sampling covariance matrix R of the uniform circular array to obtain M eigenvalues; M and Q are respectively positive integers greater than 0, Q>1, M Indicates the number of array elements included in the uniform circular array, which is equal to the number of eigenvalues obtained after eigendecomposing the sampling covariance matrix R of the uniform circular array;

Step 2, calculate the MUSIC spectrum of the signal with the incident direction (θ, φ), and then set the initial value of the mutual coupling matrix of the uniform circular array, and then obtain the initial values of Q azimuth angles of the Q incident signals, respectively q ∈ {0,1,2,...,Q-1}, Indicates the initial value of the azimuth angle of the q+1th incident signal;

Initialization: let k represent the kth correction, and the initial value of k is 1; let the mutual coupling matrix of the uniform circular array after the kth correction be C _k , and set the initial values of Q azimuth angles of the Q incident signals as the 0th The azimuth angle θ ₀ of the Q incident signals after the second correction; the initial value of the mutual coupling matrix of the uniform circular array is set to C ₀ , C ₀ =I _M , and I _M represents the M×M dimensional identity matrix;

Step 3: According to the mutual coupling matrix C _k of the uniform circular array after the k-th correction, the direction of arrival is estimated for the Q incident signals respectively, and the MUSIC spectrum P of the signal whose incident direction is (θ _k , φ) after the k-th correction is obtained _MUSIC (θ _k ,φ), and the azimuth angles of the Q incident signals after the kth correction;

Step 4, sequentially obtain the definition formula and calculation formula of the reciprocal sum J _ck of the MUSIC spectrum values of the Q incident signals after the k-th correction, and then calculate the mutual coupling matrix C _k of the uniform circular array after the k-th correction;

Step 5, increase k by 1, return to step 3, until J _ck -J _c(k-1) <△, then the correction iteration ends, J _c(k-1) represents the Q incident signals after the k-1th correction The sum of the reciprocals of the MUSIC spectrum values of , △ represents the set threshold value, and the mutual coupling matrix C _k of the uniform circular array corresponding to the kth correction when the correction iteration stops is recorded as the final mutual coupling matrix of the uniform circular array matrix The azimuth angles of the Q incident signals corresponding to the kth correction when the correction iteration stops are recorded as the final azimuth angles of the Q incident signals

Step 6, according to the final mutual dual matrix of the uniform circular array and the final azimuths of the Q incident signals Calculate the interference plus noise covariance matrix of the reconstructed uniform circular array

Step 7, calculate the final steering vector of the desired signal as And according to the interference plus noise covariance matrix of the uniform circular array after reconstruction The weight vector of the adaptive beamformer of the uniform circular array is calculated as w, and then the beamforming design of the uniform circular array interference plus noise covariance matrix reconstruction based on iterative mutual coupling correction is completed.

Beneficial effects of the present invention: First, the present invention uses the DOA and uniform circular array mutual coupling matrix iterative estimation method to more accurately estimate the two indispensable factors in the reconstruction of the interference plus noise covariance matrix under the influence of mutual coupling The parameters, that is, the mutual coupling matrix of the uniform circular array and the azimuth angle of the interference signal, make the reconstruction of the interference plus noise covariance matrix fully carry the mutual coupling information, and improve the robustness of the beamformer under the influence of mutual coupling; Second, the present invention reconstructs the interference covariance matrix by taking discrete points instead of integrals in the interference angle area, which reduces the computational complexity and improves the real-time performance of the algorithm.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. Those skilled in the art can also obtain other drawings based on these drawings without creative work.

Fig. 1 is a flow chart of a radar covariance matrix reconstruction beamforming method based on iterative mutual coupling correction of the present invention;

Fig. 2 is that the method performance of the present invention varies with the signal-to-noise ratio (SNR) when there is an observation error under the mutual coupling condition;

Fig. 3 (a) is that there is observation error under the condition of mutual coupling and the input SNR is 20dB when the method performance of the present invention changes with sample number;

Fig. 3 (b) is that there is observation error under the condition of mutual coupling and input signal-to-noise ratio is -5dB when the method performance of the present invention changes with sample number;

Fig. 4 is when there is no observation error under the condition of mutual coupling, the method performance of the present invention changes curve figure with SNR;

Fig. 5 (a) is no observation error under the condition of mutual coupling and the input signal-to-noise ratio is 20dB when the method performance of the present invention changes with sample number curve;

Fig. 5(b) is a graph showing the variation of the performance of the method of the present invention with the number of samples when there is no observation error and the input signal-to-noise ratio is -5dB under mutual coupling conditions.

Detailed ways

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

Referring to Fig. 1, it is a flow chart of a radar covariance matrix reconstruction beamforming method based on iterative mutual coupling correction of the present invention; wherein the radar covariance matrix reconstruction beamforming method based on iterative mutual coupling correction comprises the following steps :

Step 1, determine the uniform circular array, the uniform circular array includes M array elements, obtain the sampling covariance matrix R of the uniform circular array, perform eigendecomposition on the sampling covariance matrix R of the uniform circular array, and obtain M eigenvalues ; Where M is a positive integer greater than 0.

Specifically, a uniform circular array is determined, the uniform circular array includes M array elements, there are Q signal sources within the set range of the uniform circular array, and the Q signal sources transmit Q incident signals to the uniform circular array, and the Q incident signals The signal includes 1 desired signal and Q-1 interference signals; the set range is within S kilometers from the uniform circular array, and S is a positive integer greater than 0; the value of S is 100 in this embodiment.

The pitch angle of the Q incident signals relative to the uniform circular array is φ, φ={φ ₀ ,φ ₁ ,…,φ _q ,…,φ _Q-1 }, q∈{0,1,…,Q-1} , φ _q represents the pitch angle of the q+1th incident signal relative to the uniform circular array, and the values of φ ₀ , φ ₁ , ..., φ _q , ..., φ _Q-1 are equal; φ ₀ represents the desired signal relative to The pitch angles of the uniform circular array, the pitch angles of the Q-1 interference signals relative to the uniform circular array are φ ₁ , φ ₂ , ..., φ _Q-1 respectively.

The echo data received by the uniform circular array is acquired, and autocorrelation processing is performed on the echo data received by the uniform circular array to obtain a sampling covariance matrix R of the uniform circular array.

Under the premise that the number of expected signals is 1, the number of interference signals is Q-1, and the pitch angle of Q incident signals relative to the uniform circular array is φ, the sampling covariance matrix R of the uniform circular array is characterized Decompose to obtain M eigenvalues; since the number of array elements of the uniform circular array is M, the number of eigenvalues obtained after eigendecomposition is also M.

The M eigenvalues obtained after eigendecomposition are sorted from large to small, and the first Q eigenvalues of the M eigenvalues sorted from large to small are recorded as Q large eigenvalues, and the remaining M-Q eigenvalues are The value is recorded as M-Q small eigenvalues; the eigenvectors corresponding to the first Q large eigenvalues are used as the desired signal plus interference subspace, and the eigenvectors corresponding to M-Q small eigenvalues are recorded as the noise subspace, then for the uniform circle The sampling covariance matrix R of the array is subjected to eigendecomposition, and its decomposition form is:

Among them, R is the sampling covariance matrix of the uniform circular array, and its dimension is M×M; Λ _SI is a diagonal matrix formed by the Q large eigenvalues respectively being diagonal elements, and U _SI is the characteristic corresponding to the Q large eigenvalues The desired signal plus interference subspace formed by the vector, Λ _N is a diagonal matrix formed by MQ small eigenvalues respectively as diagonal elements, U _N is the noise subspace formed by the eigenvectors corresponding to MQ small eigenvalues, superscript H Represents the conjugate transpose operation, M and Q are positive integers greater than 0, M>Q; M represents the number of array elements included in the uniform circular array, which is obtained after eigendecomposition of the sampling covariance matrix R of the uniform circular array The number of eigenvalues of is equal.

Step 2, calculate the MUSIC spectrum of the signal with the incident direction (θ, φ), and then set the initial value of the mutual coupling matrix of the uniform circular array, then the MUSIC spectrum of the signal with the incident direction (θ, φ) has an initial estimated value ; Substitute the initial value of the mutual coupling matrix of the uniform circular array into the expression of the signal MUSIC spectrum P _MUSIC (θ, φ) with the incident direction (θ, φ), and search for the MUSIC spectrum peak within the set azimuth angle range, and then get The initial values of Q azimuth angles for the Q incident signals are respectively

Specifically, the signal MUSIC spectrum P _MUSIC (θ, φ) whose incident direction is (θ, φ) is expressed as:

Among them, θ represents the azimuth angle of the Q incident signals, φ represents the elevation angle of the Q incident signals relative to the uniform circular array, a(θ, φ) is the signal steering vector with the incident direction (θ, φ), and C is the uniform The mutual coupling matrix of the circular array, and the mutual coupling matrix C of the uniform circular array is unknown; U _N is the noise subspace formed by the eigenvectors corresponding to MQ small eigenvalues, and the superscript H represents the conjugate transpose operation.

Set the initial value C ₀ of the mutual coupling matrix of the uniform circular array, C ₀ =I _M , I _M represents the M×M dimensional unit matrix; substitute the initial value C ₀ of the mutual coupling matrix of the uniform circular array into the incident direction as (θ,φ ) signal MUSIC spectrum P _MUSIC (θ, φ) expression, and search the MUSIC spectrum peak in the range of 0° to 180° azimuth angle, and then get the initial values of Q azimuth angles of Q incident signals, respectively Indicates the initial value of the azimuth angle of the q+1th incident signal; wherein, the range of the set azimuth angle is within the range of 0° to 180°.

Initialization: Let k represent the kth correction, and the initial value of k is 1; and the initial value of the Q azimuth angles of the Q incident signals is taken as the azimuth angle θ ₀ of the Q incident signals after the 0th correction; set the uniform circle The initial value of the mutual coupling matrix of the array is C ₀ , C ₀ =I _M , and I _M represents the M×M dimensional identity matrix.

Step 3, after the eigendecomposition is completed, in the case of considering the mutual coupling of the uniform circular array, let the mutual coupling matrix of the uniform circular array after the k-th correction be C _k , and according to the mutual coupling matrix of the uniform circular array after the k-th correction C _k uses the MUSIC spectrum estimation method to estimate the direction of arrival (DOA) of the Q incident signals respectively, and obtain the signal MUSIC spectrum P _MUSIC (θ _k , φ) with the incident direction (θ _k , φ) after the kth correction.

Specifically, in the case of considering the mutual coupling of the uniform circular array, according to the mutual coupling matrix C _k of the uniform circular array after the kth correction, the MUSIC spectrum estimation method is used to calculate the direction of arrival (DOA) of the incident desired signal and Q-1 interference signals (DOA) estimation, calculate the signal MUSIC spectrum P _MUSIC (θ _k ,φ) with the incident direction (θ _k ,φ) after the kth correction, and its expression is:

Among them, θ _k represents the azimuth angle of the Q incident signals after the kth correction, φ represents the elevation angle of the Q incident signals relative to the uniform circular array, and a(θ _k , φ) is the incident direction as (θ _k , φ) , C _k is the mutual coupling matrix of the uniform circular array after the k-th correction, and the mutual coupling matrix of the uniform circular array after the k-th correction is unknown; U _N is the eigenvector corresponding to the MQ small eigenvalues The noise subspace formed, the superscript H indicates the conjugate transpose operation.

Since the mutual coupling matrix C of the uniform circular array after the k-th correction is unknown, the signal MUSIC spectrum P _MUSIC (θ _k ,φ) with the incident direction (θ _k ,φ) cannot be calculated, then the waves of the desired signal and the interference signal The direction of arrival (DOA) is unknown.

Search for the MUSIC spectrum peak of the signal MUSIC spectrum P _MUSIC (θ _k , φ) with the incident direction (θ _k , φ) after the k-th correction within the range of the set azimuth angle, and obtain the MUSIC spectrum peak of the Q incident signal after the k-th correction The azimuth angle is θ _k , θ _k ={θ _0k ,θ _1k ,…,θ _qk ,…,θ _(Q-1)k }, q∈{0,1,…,Q-1}, θ _qk represents the The azimuth angle of the q+1th incident signal after the k-th correction; θ _0k represents the azimuth angle of the expected signal after the k-th correction, θ _1k , θ _2k ,…, θ _(Q-1)k is the k-th correction The azimuth angles of Q-1 interference signals; wherein, the set azimuth angles range from 0° to 180°.

Step 4, define the sum of the reciprocals of the MUSIC spectrum values of the Q incident signals after the k-th correction as J _ck , from step 3, when the mutual coupling matrix of the uniform circular array after the k-th correction and the actual uniform circular array If the values of the coupling matrices are equal, the sum J _ck of the reciprocals of the MUSIC spectrum values of the Q incident signals after the k-th correction has the minimum value; if the mutual coupling matrix of the uniform circular array and the actual uniform circular array after the k-th correction If the values of the coupling matrices are not equal, the sum J _ck of the reciprocals of the MUSIC spectrum values of the Q incident signals after the kth correction has no minimum value; then, if the Q azimuths of the Q incident signals after the kth correction have been , let the sum J _ck of the reciprocals of the MUSIC spectrum values of the Q incident signals after the k-th correction be the smallest, and then calculate the mutual coupling matrix C _k of the uniform circular array after the k-th correction.

Step 4 specifically includes the following sub-steps:

(4a) According to the mutual coupling matrix C _k of the uniform circular array after the k-th correction, the sum of the reciprocals of the MUSIC spectrum values of the Q incident signals after the k-th correction is defined as J _ck , and the definition expression is:

in, Indicates that the direction of incidence is The signal steering vector of , φ _q represents the pitch angle of the q+1th incident signal relative to the uniform circular array, Indicates the azimuth angle of the q+1th incident signal after the kth correction, |||| ² represents the square operation after taking the modulus value; C _k is the mutual coupling matrix of the uniform circular array after the kth correction, U _N is the noise subspace formed by the eigenvectors corresponding to MQ small eigenvalues, and the superscript H represents the conjugate transpose operation.

It can be seen from step 3 that when the initial estimated value of the mutual coupling matrix of the uniform circular array is not equal to the value of the actual mutual coupling matrix of the uniform circular array, the reciprocal of the MUSIC spectrum values of the Q incident signals after the kth correction The sum of J _ck has no minimum value; then, in the case that Q azimuth angle estimates of the Q incident signals after the k-th correction have been obtained, let the sum of the reciprocals of the MUSIC spectrum values of the Q incident signals after the k-th correction be taken as The value is the smallest, to modify the mutual coupling matrix of the uniform circular array, that is, to solve the mutual coupling of the uniform circular array after the kth correction corresponding to the reciprocal of the MUSIC spectrum values of the Q incident signals after the kth correction and the value of J _ck is the smallest matrix.

(4b) Because the mutual coupling matrix of the uniform circular array has some special properties: first, the mutual coupling matrix of the uniform circular array is a symmetrical matrix; second, the greater the distance between two adjacent array elements of the uniform circular array, the greater the mutual The smaller the mutual impedance between; third, the closed geometric structure of the uniform circular array, that is, the mutual impedance of the array element numbered 2 to the array element numbered 1, and the array element numbered 1 to the array element numbered 2 The mutual impedance values of the array elements are equal.

Based on the above characteristics, the mutual coupling matrix C _k of the uniform circular array after the k-th correction is a complex circular symmetric matrix, which can be obtained from the first LC in the first row of the mutual coupling matrix _{C k} of the uniform circular array after the k-th correction elements are fully identified, Represents the rounding down operation; and determine the product of the mutual coupling matrix C _k of the uniform circular array after the kth correction and the signal steering vector a(θ _k , φ) with the incident direction (θ _k , φ), which is equivalent to The M×L _C -dimensional matrix Q[a(θ _k ,φ)] composed of M elements in the signal steering vector a(θ _k ,φ) with the incident direction (θ _k ,φ) is equal to The product of _LC × 1-dimensional vector c _k formed by the first LC elements of the first row in the mutual coupling matrix _{C k} of the circular array, that is, C _k a(θ _k ,φ)=Q[a(θ _k , φ)] c _k .

Among them, c _k is the _LC × 1-dimensional vector composed of the first LC elements in the first row of the mutual coupling matrix _{C k} of the uniform circular array after the k-th correction, c _dk represents the d+1th element in the first row of the mutual coupling matrix C _k of the uniform circular array after the kth correction, and the superscript T represents the transpose operation.

The M×L _C -dimensional matrix Q[a(θ _k ,φ)] composed of M elements in the signal steering vector a(θ _k ,φ) with the incident direction (θ _k ,φ) is modified by the kth The first M×L _C -dimensional matrix Q _1k , the second M×L _C -dimensional matrix Q _2k after the k-th correction, the third M×L _C -dimensional matrix Q _3k after the k-th correction, and the k-th correction The fourth M×L _C -dimensional matrix Q _4k is obtained by adding, that is, Q[a(θ _k ,φ)]=Q _1k +Q _2k +Q _3k +Q _4k , the first M×L after the kth correction _C -dimensional matrix Q _1k , the second M×L _C -dimensional matrix Q _2k after the k-th correction, the third M×L _C -dimensional matrix Q _3k after the k-th correction, and the fourth M×L C-dimensional matrix Q 3k after the k-th correction The L _C -dimensional matrix Q _4k is composed of the elements in the signal-steering vector a(θ _k , φ) with the incident direction (θ _k , φ), where the first M×L _C -dimensional matrix Q _1k after the kth correction The element in row r and column h in is Q _1(r,h)k , and the element in row r' and column h' in the second M×L _C -dimensional matrix Q _2k after the kth correction is Q _{2( r',h')k} , the third M×L _C -dimensional matrix Q ₃ after the k-th correction, the elements in the r"th row and the h"th column are Q _3(r",h")k , the k-th The element in row r"' and column h"' in the fourth M×L _C -dimensional matrix Q ₄ after modification is Q _4(r"',h"')k , and the expressions are respectively:

Among them, r∈{1,2,…,row _1k }, h∈{1,2,…,col _1k }, row _1k represents the number of rows of the first M×L _C -dimensional matrix Q _1k after the kth correction , col _1k represents the number of columns of the first M×L _C -dimensional matrix Q _1k after the kth correction, r'∈{1,2,...,row _2k }, h'∈{1,2,...,col _2k }, row _2k represents the row number of the second M×L _C -dimensional matrix Q _2k after the k-th correction, col _2k represents the column number of the second M×L _C -dimensional matrix Q _2k after the k-th correction, r” ∈{1,2,…,row _3k }, h”∈{1,2,…,col _3k }, row _3k represents the number of rows of the third M×L _C -dimensional matrix Q _3k after the kth correction, col _3k represents the number of columns of the third M×L _C -dimensional matrix Q _3k after the kth correction, r"'∈{1,2,...,row _4k }, h"'∈{1,2,...,col _4k }, row _4k represents the number of rows of the fourth M×L _C -dimensional matrix Q _4k after the k correction, and col _4k represents the column number of the fourth M×L _C -dimensional matrix Q _4k after the k correction, Represents an upward rounding operation; a(θ _k ,φ) _r+h-1 represents the r+h-1th element in the signal steering vector a(θ _k ,φ) with the incident direction (θ _k ,φ), a (θ _k ,φ) _r'-h'+1 represents the r'-h'+1th element in the signal steering vector a(θ _k ,φ) with the incident direction (θ _k ,φ), a(θ _k ,φ) _{M+1+r”-h”} represents the M+1+r”-h”th element in the signal steering vector a(θ _k ,φ) with the incident direction (θ _k ,φ), a(θ _k , φ) _r"'+h"'-M-1 means the r"'+h"'-M-1 of the signal steering vector a(θ _k ,φ) with the incident direction (θ _k ,φ) Elements; θ _k represents the azimuth angles of the Q incident signals after the kth correction, and the azimuth angle θ ₀ of the Q incident signals after the 0th correction is the initial value of the Q azimuth angles of the Q incident signals.

(4c) From the properties of the mutual coupling matrix of the uniform circular array described in (4b), it can be obtained that the mutual coupling matrix C _k of the uniform circular array after the kth correction and the incident direction are The signal steering vector of Equivalent substitutions can be made, that is, Among them, c _k is the _LC × 1-dimensional vector composed of the first row of L _C elements of the mutual coupling matrix C _k of the uniform circular array after the k-th correction; then the Q incident signals after the k-th correction are calculated The reciprocal of the MUSIC spectrum value and J _ck , the calculation expressions are:

in, |||| ² means to calculate the square operation after taking the modulus value.

(4d) In order to solve the L _C ×1-dimensional vector c _k composed of the first L _C elements of the first row of the mutual coupling matrix C _k of the uniform circular array after the k-th correction, a linear constraint is added, assuming that the uniform circular array The internal self-impedance of the array element of the mutual dual matrix is 1, then C _k (1,1) = 1, that is, e ^H c _k = 1, where e is an L×1-dimensional vector whose first element is 1 and the rest of the elements are 0, That is, the following equation is established:

Among them, the superscript H represents the conjugate transpose operation, and s.t. represents the constraint condition.

Finally, the _LC × 1-dimensional vector c _k composed of the first LC elements of the first line of the mutual coupling matrix _{C k} of the uniform circular array after the k-th correction is calculated, and its expression is:

c _k ＝G _k ^-1 e(e ^H G _k ^-1 e) ^-1

Since the mutual coupling matrix _{C k} of the uniform circular array after the kth correction is the LC × 1-dimensional vector c _k composed of the first LC elements of the first row of the uniform circular array, it is the mutual coupling matrix _{C k} of the uniform circular array after the kth correction The _LC × 1-dimensional vector composed of the first L _C elements of the first row of , and the mutual coupling matrix C _k of the uniform circular array after the k-th correction is a complex circular symmetric matrix, so the uniform circular array after the k-th correction The elements in the mutual coupling matrix _{C k} can be completely determined by the elements in the LC ×1-dimensional vector c _k composed of the first LC elements of the first row of the mutual coupling matrix _{C k} of the uniform circular array after the kth correction.

Therefore, according to the _LC × 1-dimensional vector c _k composed of the first row of L _C elements of the mutual coupling matrix C _k of the uniform circular array after the kth correction, the mutual coupling matrix of the uniform circular array after the kth correction is calculated. Coupling matrix C _k .

Step 5, increase k by 1, return to step 3, until J _ck -J _c(k-1) <△, then the correction iteration ends, J _c(k-1) represents the Q incident signals after the k-1th correction The sum of the reciprocals of the MUSIC spectrum values of , △ represents the set threshold value, and the value of △ in this embodiment is 0.0001; and the mutual coupling matrix C _k of the uniform circular array corresponding to the kth correction when the correction iteration stops is respectively , denoted as the final mutual dual matrix of the uniform circular array The azimuth θ _k of the Q incident signals corresponding to the k-th correction when the correction iteration stops is recorded as the final azimuth angle of the Q incident signals Indicates the final azimuth angle of the q+1th incident signal after correction; then the Q final incident directions of the Q incident signals are obtained, respectively: φ _q represents the pitch angle of the q+1th incident signal relative to the uniform circular array; where, is the final incident direction of the desired signal.

Step 6, after obtaining the Q final incident directions of Q incident signals and the final mutual dual matrix of the uniform circular array Then start to reconstruct the interference plus noise covariance matrix of the uniform circular array; including the reconstruction of the interference covariance matrix of the uniform circular array and the reconstruction of the noise covariance matrix of the uniform circular array; and then calculate the reconstructed uniform circular array Interference-plus-noise covariance matrix.

Step 6 specifically includes the following sub-steps:

(6a) Eliminate the final incident directions of the desired signal from the Q final incident directions of the Q incident signals, and obtain the final incident directions of Q-1 interference signals, respectively

Considering the error of the spectrum estimation algorithm, the azimuth estimation error range is set to △θ, so Q-1 interference signal angle regions can be expressed as

That is, the final incident directions of the Q-1 interference signals are located in In, and Q-1 interference signal angle area Contains Q-1 discrete sampling points, each discrete sampling point corresponds to the final incident direction of an interference signal; in the Q-1 interference signal angle area Randomly select L' discrete sampling points to calculate the covariance matrix, L'≤Q-1, and then sum to obtain the interference covariance matrix of the reconstructed uniform circular array which is

Among them, ∪ represents the union operation, b(θ _l' ,φ _l' ) is the Q-1 interference signal angle area The steering vector at the l'th discrete sampling point, l'=1,2,...,L', and according to the Q final incident directions of the Q incident signals and the final mutual-dual matrix of the uniform circular array Calculate the steering vector b(θ,φ) of the desired signal after mutual coupling correction, Therefore, the interference covariance matrix of the reconstructed uniform circular array is calculated Its expression is:

Among them, R represents the sampling covariance matrix of the uniform circular array, and b(θ _l' , φ _l' ) represents Q-1 interference signal angle areas The steering vector at the l'th discrete sampling point within is equal to the signal steering vector with the incident direction (θ _l' , φ _l' ); then the interference covariance matrix reconstruction of the uniform circular array is completed.

(6b) Reconstruct the noise covariance matrix of the uniform circular array. Under ideal conditions, the M-Q small eigenvalues obtained after eigendecomposition of the sampling covariance matrix of the uniform circular array are equal to each other, and their values are the noise power values.

But in the actual situation, the MQ small eigenvalues are not equal. For the sake of simplicity, the minimum value of the eigenvalue is selected from the MQ small eigenvalues as the noise power estimation value of the uniform circular array Then calculate the noise covariance matrix of the reconstructed uniform circular array I represents an M×M dimensional identity matrix.

(6c) Reconstruct the interference plus noise covariance matrix of the uniform circular array: according to the interference covariance matrix of the uniform circular array after reconstruction and the noise covariance matrix of the reconstructed uniform circular array Calculate the interference plus noise covariance matrix of the reconstructed uniform circular array Its expression is:

Among them, R represents the sampling covariance matrix of the uniform circular array, and I represents the M×M dimensional unit matrix; then, the reconstruction of the interference-plus-noise covariance matrix of the uniform circular array is completed.

Step 7, calculate the final steering vector of the desired signal as And according to the interference plus noise covariance matrix of the uniform circular array after reconstruction Using the linear constrained minimum variance (LCMV) criterion to calculate the weight vector of the adaptive beamformer of the uniform circular array is w, and then completed the beamforming design of the uniform circular array interference plus noise covariance matrix reconstruction based on iterative mutual coupling correction .

Specifically, the final steering vector of the desired signal is calculated as is the incident direction is The signal steering vector of , is the final incident direction of the desired signal, the weight vector w of the adaptive beamformer of the uniform circular array is obtained by using the linear constrained minimum variance (LCMV) criterion, and its expression is:

Among them, the superscript -1 represents the inversion operation, and the superscript H represents the conjugate transposition operation; and then the beamforming design of the uniform circular array interference plus noise covariance matrix reconstruction based on iterative mutual coupling correction is completed.

The effects of the present invention are further verified and illustrated by the following simulation experiments.

(1) Simulation conditions

The simulation experiment of the present invention is carried out under MATLAB software, and in the experiment of the present invention, uniform circular array adopts 10 array elements, and the signal wavelength of Q incident signal is set to 0.1 meter, and adjacent array element spacing d and Q incident The signal wavelength ratio d/λ of the signal is 0.5, the pitch angle of each incident signal relative to the uniform circular array is set to 30°, the azimuth angle of the desired signal is set to 95°, two interference signals are set, and two interference signals The azimuth angles of the signals are 50° and 140°, respectively.

The specific algorithm parameters are shown in the table below:

(2) Simulation content and result analysis

In order to illustrate the superiority of the algorithm of the present invention, Figures 2 to 5 show the processing results of several other beamforming algorithms, including optimal beamformers, sampling matrix inversion (SMI) beamformers, and covariance matrix reconstruction Algorithms and worst-case performance optimization methods.

The horizontal axis in Fig. 2 represents the input SNR, and the vertical axis represents the output SINR; Fig. 2 shows that there are signal observation errors, the number of sampling snapshots is 30, and the output SINR of several beamforming methods varies with the expected signal input The curve of the signal-to-interference-to-noise ratio change. From Figure 2, we can see that in the presence of mutual coupling effects and incident signal observation errors, the performance of the ordinary covariance matrix reconstruction method drops sharply, and the performance in low signal-to-noise ratio scenarios is even far inferior to the SMI method ; The worst performance optimization beamforming method maintains better performance robustness, but when the expected signal power becomes stronger, the gap between its performance and the theoretical optimal value is increasing; and the covariance based on mutual coupling correction proposed by the present invention The performance of the matrix reconstruction method is very close to the theoretical optimal value under the condition of high signal-to-noise ratio, and the performance of the algorithm decreases under the condition of low signal-to-noise ratio, because the DOA estimation will occur when the expected signal power is lower than the noise level misalignment, thereby affecting the performance of the beamformer.

The horizontal axis of Figure 3(a) and Figure 3(b) represents the number of sampling samples, and the vertical axis represents the output signal-to-interference-noise ratio of the beamformer; Figure 3(a) shows that there is a signal observation error and the input signal-to-noise ratio is 20dB Figure 3(b) shows the simulation results when there are signal observation errors and the input signal-to-noise ratio is -5dB. Simulation results show that when the input signal-to-noise ratio of the desired signal is relatively high, the performance of the beamforming method proposed by the present invention is significantly superior to other beamforming methods; The beamforming algorithm still has very good performance.

The horizontal axis of Fig. 4 represents the input SNR, and the vertical axis represents the output SINR; Fig. 4 shows that there is no signal observation error, the number of sampling snapshots is 30, and the output SINR of several beamforming methods varies with the expected signal Input the curve of SINR change. From Figure 4, we can see that under the condition that only the mutual coupling of the uniform circular array is considered to cause the steering vector mismatch between the desired signal and the interference signal, after the mutual coupling correction by this method, the performance of the beamformer is at a high SNR In this case, there is almost no gap with the theoretical optimal value, because this method only corrects for mutual coupling factors, and eliminates the expected signal component in the sampling covariance matrix, and can achieve close to Theoretical optimal performance.

The horizontal axis of Figure 5(a) and Figure 5(b) represents the number of sampling samples, and the vertical axis represents the output signal-to-interference-noise ratio of the beamformer; Figure 5(a) shows that there is no signal observation error and the input signal-to-noise ratio is 20dB Figure 3(b) shows the simulation results when there is no signal observation error and the input signal-to-noise ratio is -5dB. The results show that under the condition that the mutual coupling of the uniform circular array is considered, the performance of the method of the present invention is better than that of the signal observation error.

In summary, the simulation experiment has verified the correctness, effectiveness and reliability of the present invention.

The above is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Anyone skilled in the art can easily think of changes or substitutions within the technical scope disclosed in the present invention. Should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the protection scope of the claims.

Claims (4)

1. A radar covariance matrix reconstruction beamforming method based on iterative mutual coupling correction, is characterized in that, comprises the following steps: Step 1, determine the uniform circular array, the uniform circular array includes M array elements, there are Q signal sources within the set range of the uniform circular array, and the Q signal sources transmit Q incident signals to the uniform circular array, and the Q incident signals The signal contains 1 desired signal and Q-1 interference signals; Obtain the sampling covariance matrix R of the uniform circular array, and perform eigendecomposition on the sampling covariance matrix R of the uniform circular array to obtain M eigenvalues; M and Q are positive integers greater than 0, Q>1, M Indicates the number of array elements included in the uniform circular array, which is equal to the number of eigenvalues obtained after eigendecomposing the sampling covariance matrix R of the uniform circular array; Step 2, calculate the MUSIC spectrum of the signal with the incident direction (θ, φ), and then set the initial value of the mutual coupling matrix of the uniform circular array, and then obtain the initial values of Q azimuth angles of the Q incident signals, respectively q ∈ {0,1,2,...,Q-1}, Indicates the initial value of the azimuth angle of the q+1th incident signal; Initialization: let k represent the kth correction, and the initial value of k is 1; let the mutual coupling matrix of the uniform circular array after the kth correction be C _k , and set the initial values of Q azimuth angles of the Q incident signals as the 0th The azimuth angle θ ₀ of the Q incident signals after the second correction; the initial value of the mutual coupling matrix of the uniform circular array is set to C ₀ , C ₀ =I _M , and I _M represents the M×M dimensional identity matrix; Step 3: According to the mutual coupling matrix C _k of the uniform circular array after the k-th correction, the direction of arrival is estimated for the Q incident signals respectively, and the MUSIC spectrum P of the signal whose incident direction is (θ _k , φ) after the k-th correction is obtained _MUSIC (θ _k ,φ), and the azimuth angles of the Q incident signals after the kth correction; Step 4, sequentially obtain the definition formula and calculation formula of the reciprocal sum J _ck of the MUSIC spectrum values of the Q incident signals after the k-th correction, and then calculate the mutual coupling matrix C _k of the uniform circular array after the k-th correction; Step 5, increase k by 1, and return to step 3 until J _ck -J _c(k-1) <Δ, then the correction iteration ends, and J _c(k-1) represents the Q incident signals after the k-1th correction The sum of the reciprocals of the MUSIC spectrum values of , Δ represents the set threshold value, and the mutual coupling matrix C _k of the uniform circular array corresponding to the kth correction when the correction iteration stops is recorded as the final mutual coupling matrix of the uniform circular array matrix The azimuth angles of the Q incident signals corresponding to the kth correction when the correction iteration stops are recorded as the final azimuth angles of the Q incident signals Step 6, according to the final mutual dual matrix of the uniform circular array and the final azimuths of the Q incident signals Calculate the interference plus noise covariance matrix of the reconstructed uniform circular array Step 7, calculate the final steering vector of the desired signal, and according to the interference-plus-noise covariance matrix of the reconstructed uniform circular array The weight vector of the adaptive beamformer of the uniform circular array is calculated as w, and then the beamforming design of the uniform circular array interference plus noise covariance matrix reconstruction based on iterative mutual coupling correction is completed; Wherein, in step 1, the Q incident signals also include: The pitch angle of the Q incident signals relative to the uniform circular array is φ, φ={φ ₀ ,φ ₁ ,…,φ _q ,…,φ _Q-1 }, q∈{0,1,…,Q-1} , φ _q represents the pitch angle of the q+1th incident signal relative to the uniform circular array, and the values of φ ₀ , φ ₁ , ..., φ _q , ..., φ _Q-1 are equal; φ ₀ represents the desired signal relative to The pitch angle of the uniform circular array, the pitch angles of the Q-1 interference signals relative to the uniform circular array are φ ₁ , φ ₂ , ..., φ _Q-1 respectively; Carry out eigendecomposition to the sampling covariance matrix R of described uniform circular array, its decomposition form is: Among them, R is the sampling covariance matrix of the uniform circular array, and its dimension is M×M; Λ _SI is a diagonal matrix formed by the Q large eigenvalues respectively being diagonal elements, and U _SI is the characteristic corresponding to the Q large eigenvalues The desired signal plus interference subspace formed by the vector, Λ _N is a diagonal matrix formed by MQ small eigenvalues respectively as diagonal elements, U _N is the noise subspace formed by the eigenvectors corresponding to MQ small eigenvalues, superscript H Represents the conjugate transposition operation, M and Q are positive integers greater than 0, M>Q; M represents the number of array elements included in the uniform circular array, which is obtained by performing eigendecomposition on the sampling covariance matrix R of the uniform circular array The number of eigenvalues of is equal; In step 2, said incident direction is the signal MUSIC spectrum P _MUSIC (θ, φ) of (θ, φ), its expression is: Among them, θ represents the azimuth angle of the Q incident signals, φ represents the elevation angle of the Q incident signals relative to the uniform circular array, a(θ, φ) is the signal steering vector with the incident direction (θ, φ), and C is the uniform The mutual coupling matrix of the circular array, U _N is the noise subspace formed by the eigenvectors corresponding to MQ small eigenvalues, and the superscript H represents the conjugate transpose operation; The process of obtaining Q initial values of Q azimuth angles of Q incident signals is as follows: Set the initial value C ₀ of the mutual coupling matrix of the uniform circular array, C ₀ =I _M , I _M represents the M×M dimensional unit matrix; substitute the initial value C ₀ of the mutual coupling matrix of the uniform circular array into the incident direction as (θ,φ ) signal MUSIC spectrum P _MUSIC (θ, φ) expression, and search the MUSIC spectrum peak in the range of 0° to 180° azimuth angle, and then get the initial values of Q azimuth angles of Q incident signals, respectively q ∈ {0,1,2,...,Q-1}, Indicates the initial value of the azimuth angle of the q+1th incident signal; wherein, the set azimuth angle range is within the range of 0° to 180°; In step 3, the signal MUSIC spectrum P _MUSIC (θ _k , φ) whose incident direction is (θ _k , φ) after the kth correction is expressed as: Among them, θ _k represents the azimuth angle of the Q incident signals after the kth correction, φ represents the elevation angle of the Q incident signals relative to the uniform circular array, and a(θ _k , φ) is the incident direction as (θ _k , φ) The signal steering vector of , C _k is the mutual coupling matrix of the uniform circular array after the kth correction, U _N is the noise subspace formed by the eigenvectors corresponding to MQ small eigenvalues, and the superscript H represents the conjugate transpose operation; Search for the MUSIC spectrum peak of the signal MUSIC spectrum P _MUSIC (θ _k , φ) with the incident direction (θ _k , φ) after the k-th correction within the range of the set azimuth angle, and obtain the MUSIC spectrum peak of the Q incident signal after the k-th correction The azimuth angle is θ _k , θ _k ={θ _0k ,θ _1k ,…,θ _qk ,…,θ _(Q-1)k }, q∈{0,1,…,Q-1}, θ _qk represents the The azimuth angle of the q+1th incident signal after the k-th correction; θ _0k represents the azimuth angle of the expected signal after the k-th correction, θ _1k , θ _2k ,…, θ _(Q-1)k is the k-th correction The azimuth angle of Q-1 interference signal; wherein, the set azimuth angle range is within the range of 0° to 180°; The sub-steps of step 4 are: (4a) According to the mutual coupling matrix C _k of the uniform circular array after the k-th correction, the sum of the reciprocals of the MUSIC spectrum values of the Q incident signals after the k-th correction is defined as J _ck , and the definition expression is: in, Indicates that the direction of incidence is The signal steering vector of , φ _q represents the pitch angle of the q+1th incident signal relative to the uniform circular array, Indicates the azimuth angle of the q+1th incident signal after the kth correction, || || ² represents the square operation after taking the modulus value; C _k is the mutual coupling matrix of the uniform circular array after the kth correction, U _N is the noise subspace formed by the eigenvectors corresponding to MQ small eigenvalues, and the superscript H represents the conjugate transpose operation; (4b) Determine the mutual coupling matrix C _k of the uniform circular array after the k-th correction is completely determined by the first L _C elements in the first row of the mutual coupling matrix C _k of the uniform circular array after the k-th correction, Represents the rounding down operation; and determine the product of the mutual coupling matrix C _k of the uniform circular array after the kth correction and the signal steering vector a(θ _k , φ) with the incident direction (θ _k , φ), which is equivalent to The M×L _C -dimensional matrix Q[a(θ _k ,φ)] composed of M elements in the signal steering vector a(θ _k ,φ) with the incident direction (θ _k ,φ) is equal to The product of _LC × 1-dimensional vector c _k formed by the first LC elements of the first row in the mutual coupling matrix _{C k} of the circular array, that is, C _k a(θ _k ,φ)=Q[a(θ _k , φ)] c _k ; Among them, c _k is the _LC × 1-dimensional vector composed of the first LC elements in the first row of the mutual coupling matrix _{C k} of the uniform circular array after the k-th correction, d∈{0,1,…,L _C -1}, c _dk represents the d+1th element in the first row of the mutual coupling matrix C _k of the uniform circular array after the k-th correction, and the superscript T represents the transpose operate; The M×L _C -dimensional matrix Q[a(θ _k ,φ)] composed of M elements in the signal steering vector a(θ _k ,φ) with the incident direction (θ _k ,φ) is modified by the kth The first M×L _C -dimensional matrix Q _1k , the second M×L _C -dimensional matrix Q _2k after the k-th correction, the third M×L _C -dimensional matrix Q _3k after the k-th correction, and the k-th correction The fourth M×L _C -dimensional matrix Q _4k is obtained by adding, that is, Q[a(θ _k ,φ)]=Q _1k +Q _2k +Q _3k +Q _4k , the first M×L after the kth correction _C -dimensional matrix Q _1k , the second M×L _C -dimensional matrix Q _2k after the k-th correction, the third M×L _C -dimensional matrix Q _3k after the k-th correction, and the fourth M×L C-dimensional matrix Q 3k after the k-th correction The L _C -dimensional matrix Q _4k is composed of the elements in the signal-steering vector a(θ _k , φ) with the incident direction (θ _k , φ), where the first M×L _C -dimensional matrix Q _1k after the kth correction The element in row r and column h in is Q _1(r,h)k , and the element in row r' and column h' in the second M×L _C -dimensional matrix Q _2k after the kth correction is Q _{2( r',h')k} , the third M×L _C -dimensional matrix Q ₃ after the k-th correction, the elements in the r"th row and the h"th column are Q _3(r",h")k , the k-th The element in row r"' and column h"' in the fourth M×L _C -dimensional matrix Q ₄ after modification is Q _4(r"',h"')k , and the expressions are respectively: Among them, r∈{1,2,…,row _1k }, h∈{1,2,…,col _1k }, row _1k represents the number of rows of the first M×L _C -dimensional matrix Q _1k after the kth correction , col _1k represents the number of columns of the first M×L _C -dimensional matrix Q _1k after the kth correction, r'∈{1,2,...,row _2k }, h'∈{1,2,...,col _2k }, row _2k represents the row number of the second M×L _C -dimensional matrix Q _2k after the k-th correction, col _2k represents the column number of the second M×L _C -dimensional matrix Q _2k after the k-th correction, r” ∈{1,2,…,row _3k }, h”∈{1,2,…,col _3k }, row _3k represents the number of rows of the third M×L _C -dimensional matrix Q _3k after the kth correction, col _3k represents the number of columns of the third M×L _C -dimensional matrix Q _3k after the kth correction, r"'∈{1,2,...,row _4k }, h"'∈{1,2,...,col _4k }, row _4k represents the number of rows of the fourth M×L _C -dimensional matrix Q _4k after the k correction, and col _4k represents the column number of the fourth M×L _C -dimensional matrix Q _4k after the k correction, Represents an upward rounding operation; a(θ _k ,φ) _r+h-1 represents the r+h-1th element in the signal steering vector a(θ _k ,φ) with the incident direction (θ _k ,φ), a (θ _k ,φ) _r'-h'+1 represents the r'-h'+1th element in the signal steering vector a(θ _k ,φ) with the incident direction (θ _k ,φ), a(θ _k ,φ) _{M+1+r”-h”} represents the M+1+r”-h”th element in the signal steering vector a(θ _k ,φ) with the incident direction (θ _k ,φ), a(θ _k , φ) _r"'+h"'-M-1 means the r"'+h"'-M-1 of the signal steering vector a(θ _k ,φ) with the incident direction (θ _k ,φ) element; θ _k represents the azimuth angles of the Q incident signals after the kth correction, and the azimuth angles _θ of the Q incident signals after the 0th correction are the initial values of the Q azimuth angles of the Q incident signals; (4c) Determine the mutual coupling matrix C _k of the uniform circular array after the kth correction and the incident direction as The signal steering vector of perform an equivalent substitution, that is, Among them, c _k is the _LC × 1-dimensional vector composed of the first row of L _C elements of the mutual coupling matrix C _k of the uniform circular array after the k-th correction; then the Q incident signals after the k-th correction are calculated The reciprocal of the MUSIC spectrum value and J _ck , the calculation expressions are: in, || || ² means to calculate the square operation after taking the modulus value; (4d) Establish the following equation: Among them, e is an L×1-dimensional vector whose first element is 1 and the rest of the elements are 0, the superscript H indicates the conjugate transpose operation, and s.t. indicates the constraint condition; Then calculate the _LC × 1-dimensional vector c _k composed of the first LC elements of the first line of the mutual coupling matrix _{C k} of the uniform circular array after the kth correction, and its expression is: c _k ＝G _k ^-1 e(e ^H G _k ^-1 e) ^-1 Finally, according to the _LC × 1-dimensional vector c _k composed of the first LC elements of the first row of the mutual coupling matrix _{C k} of the uniform circular array after the k-th correction, the mutual coupling of the uniform circular array after the k-th correction is calculated Matrix C _k . 2. A kind of radar covariance matrix reconstruction beamforming method based on iterative mutual coupling correction as claimed in claim 1, is characterized in that, in step 5, the final azimuth angle of the Q incident signals Specifically: Final azimuth of Q incident signals Indicates the final azimuth angle of the q+1th incident signal after correction; then the Q final incident directions of the Q incident signals are obtained, respectively: φ _q represents the pitch angle of the q+1th incident signal relative to the uniform circular array; where, is the final incident direction of the desired signal. 3. A kind of radar covariance matrix reconstruction beamforming method based on iterative mutual coupling correction as claimed in claim 2, is characterized in that, in step 6, the interference of the uniform circular array after the reconstruction adds the noise covariance matrix Its obtaining process is: (6a) Eliminate the final incident directions of the desired signal from the Q final incident directions of the Q incident signals, and obtain the final incident directions of Q-1 interference signals, respectively Set the azimuth estimation error range to Δθ, and express the Q-1 interference signal angle areas as The final incident directions of the Q-1 interference signals are located in In, and Q-1 interference signal angle area Contains Q-1 discrete sampling points, each discrete sampling point corresponds to the final incident direction of an interference signal; in the Q-1 interference signal angle area Randomly select L' discrete sampling points to calculate the covariance matrix, L'≤Q-1, and then sum to obtain the interference covariance matrix of the reconstructed uniform circular array Its expression is: Among them, ∪ represents the union operation, b(θ _l' ,φ _l' ) is the Q-1 interference signal angle area The steering vector at the l'th discrete sampling point within is equal to the value of the signal steering vector with the incident direction (θ _l' , φ _l' ); l'=1,2,...,L'; (6b) Calculate the noise covariance matrix of the reconstructed uniform circular array I represents the M×M dimensional identity matrix; where, Indicates the noise power estimate of the uniform circular array; (6c) According to the interference covariance matrix of the uniform circular array after reconstruction and the noise covariance matrix of the reconstructed uniform circular array Calculate the interference plus noise covariance matrix of the reconstructed uniform circular array Its expression is: Among them, R represents the sampling covariance matrix of the uniform circular array, and I represents the M×M dimensional identity matrix. 4. a kind of radar covariance matrix reconstruction beamforming method based on iterative mutual coupling correction as claimed in claim 3 is characterized in that, in step 7, the final steering vector of described desired signal is is the incident direction is The signal steering vector of , is the final incident direction of the desired signal; The weight vector w of the adaptive beamformer of the uniform circular array, its expression is: Among them, the superscript -1 represents the inverse operation, and the superscript H represents the conjugate transpose operation.